diff --git a/ci/build_wheel_python.sh b/ci/build_wheel_python.sh
index 92a0c8df2..22711fd04 100755
--- a/ci/build_wheel_python.sh
+++ b/ci/build_wheel_python.sh
@@ -16,7 +16,14 @@ cd "${package_dir}"
 RAPIDS_PY_CUDA_SUFFIX="$(rapids-wheel-ctk-name-gen ${RAPIDS_CUDA_VERSION})"
 CPP_WHEELHOUSE=$(RAPIDS_PY_WHEEL_NAME="rmm_${RAPIDS_PY_CUDA_SUFFIX}" rapids-download-wheels-from-s3 cpp /tmp/librmm_dist)
 
-python -m pip wheel . -w dist -vvv --no-deps --disable-pip-version-check --find-links "${CPP_WHEELHOUSE}"
+# ensure 'rmm' wheel builds always use the 'librmm' just built in the same CI run
+#
+# using env variable PIP_CONSTRAINT is necessary to ensure the constraints
+# are used when created the isolated build environment
+echo "librmm-${RAPIDS_PY_CUDA_SUFFIX} @ file://$(echo ${CPP_WHEELHOUSE}/librmm_${RAPIDS_PY_CUDA_SUFFIX}*.whl)" > ./build-constraints.txt
+
+PIP_CONSTRAINT="${PWD}/build-constraints.txt" \
+    python -m pip wheel . -w dist -vvv --no-deps --disable-pip-version-check
 
 mkdir -p final_dist
 python -m auditwheel repair -w final_dist dist/*